Abstract
For a linear differential system, we obtain formulas for the computation of the exact boundaries of upper mobility for Lyapunov exponents under exponentially decaying perturbations of its coefficient matrix on the basis of the Cauchy matrix.
Similar content being viewed by others
References
Perron, O., Die Ordnungszahlen linearer Differentialgleichungssysteme, Math. Z., 1930, vol. 31, no. 5, pp. 748–766.
Izobov, N.A., Exponential Indices of a Linear System and Their Calculation, Dokl. Akad. Nauk BSSR, 1982, vol. 26, no. 1, pp. 5–8.
Nurmatov, A.M., Neobkhodimye usloviya ustoichivosti kharakteristicheskikh pokazatelei Lyapunova lineinykh differentsial’nykh sistem pri eksponentsial’no ubyvayushchikh vozmushcheniyakh (Necessary Stability Conditions for Lyapunov Characteristic Exponents of Linear Differential Systems under Exponentially Decreasing Perturbations), Moscow, 1987, Deposited in VINITI 12.03.87, no. 1811-V 87.
Nurmatov, A.M., Necessary Stability Conditions for Lyapunov Characteristic Exponents of Linear Differential Systems under Exponentially Decreasing Perturbations, Differ. Uravn., 1989, vol. 25, no. 2, pp. 335–336.
Barabanov, E.A. and Denisenko, N.S., A Necessary and Sufficient Condition for the Stability of Lyapunov Exponents of Linear Differential Systems under Exponentially Decaying Perturbations, Differ. Uravn., 2007, vol. 43, no. 2, pp. 165–175.
Voidelevich, A.S., Evaluation of Exact Upper Bounds of Lyapunov Exponents of Linear Differential Systems under Exponentially Decreasing Perturbations of Coefficient Matrices, Differ. Uravn., 2013, vol. 49, no. 11, pp. 1511–1512.
Bylov, B.F., Vinograd, R.E., Grobman, D.M., and Nemytskii, V.V., Teoriya pokazatelei Lyapunova i ee prilozheniya k voprosam ustoichivosti (Theory of Lyapunov Exponents and Its Application to Problems of Stability), Moscow: Nauka, 1966.
Vinograd, R.E., On the Central Characteristic Index of a System of Differential Equations, Mat. Sb., 1957, vol. 42, no. 2, pp. 207–222.
Millionshchikov, V.M., Structurally Stable Properties of Linear Systems of Differential Equations, Differ. Uravn., 1969, vol. 5, no. 10, pp. 1775–1784.
Bylov, B.F. and Izobov, N.A., Necessary and Sufficient Conditions for the Stability of the Characteristic Exponents of a Linear System, Differ. Uravn., 1969, vol. 5, no. 10, pp. 1794–1803.
Sergeev, I.N., Sharp Upper Bounds of Mobility of the Lyapunov Exponents of a System of Differential Equations and the Behavior of the Exponents under Perturbations Approaching, Differ. Uravn., 1980, vol. 16, no. 3, pp. 438–448.
Sergeev, I.N., On the Theory of Lyapunov Exponents of Linear Systems of Differential Equations, Tr. Semin. im. I.G. Petrovskogo, 1983, vol. 9, pp. 111–166.
Millionshchikov, V.M., A Proof of the Accessibility of the Central Exponents of Linear Systems, Sibirsk. Mat. Zh., 1969, vol. 10, no. 1, pp. 99–104.
Millionshchikov, V.M., Systems with Integral Division Which Are Everywhere Dense in the Set of All Linear Systems of Differential Equations, Differ. Uravn., 1969, vol. 5, no. 7, pp. 1167–1170.
Barabanov, E.A., A Generalization of Bylov’s Reducibility Theorem and Some of Its Applications, Differ. Uravn., 2007, vol. 43, no. 12, pp. 1592–1596.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.S. Voidelevich, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 10, pp. 1312–1324.
Rights and permissions
About this article
Cite this article
Voidelevich, A.S. Exact boundaries of upper mobility of the Lyapunov exponents of linear differential systems under exponentially decaying perturbations of the coefficient matrices. Diff Equat 50, 1300–1313 (2014). https://doi.org/10.1134/S0012266114100036
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0012266114100036